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68o                        Weight of Fly Wheel.

keeping the fluctuation of velocity within a certain percentage of
the mean. Let v  mean velocity, and let

Total fluctuation of velocity = -7 of v


then the value of k 'depends on the regularity required, and
may vary from 100 for very steady driving, to 20 where constant
speed is of little value. With feet and seconds units, let z^ be
maximum velocity and z>2 minimum velocity of the fly wheel at its
mean radius, consequent on absorbing and delivering the given
^energy, and let E represent the energy area, or the 49,560 foot
pounds of Fig. 662, while the velocity falls from v^ to v%.

j      z*> (V ~ z>22)
Energy delivered =  ^ - ^


where w is the weight of the fly wheel. But this energy is equal
to the area E,


NOW Vl - 7/2 = V   X  -                   flj + V2 = 2 V

27T RN

and     v =  - -

R being radius of gyration of fly wheel.
Putting also the fly-wheel weight in tons,

-        (#! + V%) (7^ - V^) 2240         2 V2 X 2 240

&32'2 ^ 60 x 60               E^


Generally R may be taken at centre of * rim section, but if
great accuracy be required, assume a fly-wheel section, replac-
ing the arms by a thin disc of equal weight : then, moment of
inertia ,of volume (second moment) of a solid of revolution, or
JT= volume xR2, which is the third moment of the generating